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One can specify the following mathematical characteristics in each of the five Platonic solids:

1. The radius of the sphere circumscribing the polyhedron;

2. The radius of the sphere inscribed in the polyhedron;

3. The surface area of the polyhedron;

4. The volume of the polyhedron.

**polyhedron** is a solid bounded by flat polygons, which are called **faces. **The sides of the faces are called **edges**, and their corners are called **vertices**. Depending on the number of faces one can specify a tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be **convex** if it is located on one side of the plane of each of its faces. A polyhedron is called **regular** if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There are five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron.

Studio Artemy Lebedev (makes the design for the leading search engine Yandex) was proposed form of a birdhouse in the form of a polyhedron.

The correct polyhedron, the icosahedron, was chosen as the geometric shape.